Replacing Numbers with Letters

Videos to help Grade 6 students learn how to replace numbers with letters in an expression. They will also discover the commutative properties of addition and multiplication, the additive identity property of zero, and the multiplicative identity property of one.

How many of those statements would be true if the number 4 was replaced with the number 7 in each of the number sentences?

Would the number sentences be true if we were to replace the number 4 with any other number?

What if we replaced the number 4 with the number 0? Would each of the number sentences be true?

Division by zero is undefined. You cannot make zero groups of objects, and group size cannot be zero.

It appears that we can replace the number 4 with any non-zero number and each of the number sentences will be true.

A letter in an expression can represent a number. When that number is replaced with a letter, an expression is stated.

Example 1: Additive Identity Property of Zero

g + 0 = g

Remember a letter in a mathematical expression represents a number. Can we replace with any number?

Choose a value for g and replace with that number in the number sentence. What do you observe?

Is the number sentence true for all values of g?

Write the mathematical language for this property below:

Additive Identity Property of Zero: Any number added to zero equals itself. The number’s identity does not change.

Example 2: Multiplicative Identity Property of One

g × 1 = g

Remember a letter in a mathematical expression represents a number. Can we replace with any number?

Choose a value for g and replace with that number in the number sentence. What do you observe?

Is the number sentence true for all values of g?

Write the mathematical language for this property below:

Multiplicative Identity Property of One: Any number multiplied by 1 equals itself. The number’s identity does not change.

Example 3: Commutative Property of Addition and Multiplication

3 + 4 = 4 + 3
3 × 4 = 4 × 3
3 + 3 + 3 + 3 = 4 × 3
3
÷ 4 = 3/4

Replace the 3s in these equations with the letter a.

Choose a value for and replace a with that number in each of the number sentences. What do you observe?

Are the number sentences true for all values of ? Experiment with different values before making your claim.

Now write the number sentences again, this time replacing the number 4 with a variable, b.

Are the first two number sentences true for all values of and ? Experiment with different values before making your claim.

Write the mathematical language for this property below:

Commutative property of addition and commutative property of multiplication. These are sometimes called the “any-order properties”.

Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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